An electric two-wheeled vehicle which runs with a rear wheel thereof driven by an electric motor is known. As such an electric two-wheeled vehicle, a two-wheeled motor vehicle in which a battery is cooled by a cooling fan in order to prevent a temperature rise due to heat accompanying charge and discharge of the battery supplying electric power to the electric motor, has been already known as disclosed in Patent Document 1 and Patent Document 2. The vehicle disclosed in Patent Document 1 is formed so that air taken from the front of the vehicle by fans provided in a front portion and an upper portion of a battery case can be introduced into the battery case. The vehicle disclosed in Patent Document 2 is formed so that cooling air can be introduced into a battery case by the action of an electric fan through an opening located at a lower portion of the battery case.    Patent Document 1: Japanese Patent Application Laid-open No. 2003-002273    Patent Document 2: International Patent Application Publication No. WO 2004/069638